Chapter 2, Problem 94A

(a)

Interpretation Introduction

Interpretation:

The percent error of density measurement $\text{8}\text{.86}\text{g/mL}$ of copper needs to be determined, if the accepted density is $\text{8}\text{.96}\text{g/mL}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 94A

The percent error value of density measurement of copper is $1.12\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{8}\text{.86}\text{g/mL}$ while the accepted value is $\text{8}\text{.96}\text{g/mL}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{8}\text{.86}\text{g/mL}-\text{8}\text{.96}\text{g/mL}\right|}{\text{8}\text{.96}\text{g/mL}}\right)\times 100\\ =\left(\frac{\left|-0.10\text{g/mL}\right|}{\text{5}\text{.5 g/mL}}\right)\times 100\\ =1.12\%\end{array}$

Hence, the percent error is $1.12\%$.

(b)

Interpretation Introduction

Interpretation:

The percent error of density measurement $\text{8}\text{.92}\text{g/mL}$ of copper needs to be determined, if the accepted density is $\text{8}\text{.96}\text{g/mL}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 94A

The percent error value of density measurement of copper is $0.446\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{8}\text{.86}\text{g/mL}$ while the accepted value is $\text{8}\text{.96}\text{g/mL}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{8}\text{.92}\text{g/mL}-\text{8}\text{.96}\text{g/mL}\right|}{\text{8}\text{.96}\text{g/mL}}\right)\times 100\\ =\left(\frac{\left|-0.04\text{g/mL}\right|}{\text{5}\text{.5 g/mL}}\right)\times 100\\ =0.446\%\end{array}$

Hence, the percent error is $0.446\%$.

(c)

Interpretation Introduction

Interpretation:

The percent error of density measurement $\text{9}\text{.00}\text{g/mL}$ of copper needs to be determined, if the accepted density is $\text{8}\text{.96}\text{g/mL}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 94A

The percent error value of density measurement of copper is $0.446\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{9}\text{.00}\text{g/mL}$ while the accepted value is $\text{8}\text{.96}\text{g/mL}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{9}\text{.00}\text{g/mL}-\text{8}\text{.96}\text{g/mL}\right|}{\text{8}\text{.96}\text{g/mL}}\right)\times 100\\ =\left(\frac{\left|0.04\text{g/mL}\right|}{\text{5}\text{.5}\text{g/mL }}\right)\times 100\\ =0.446\%\end{array}$

Hence, the percent error is $0.446\%$.

(d)

Interpretation Introduction

Interpretation:

The percent error of density measurement $\text{8}\text{.98}\text{g/mL}$ of copper needs to be determined, if the accepted density is $\text{8}\text{.96}\text{g/mL}$.

Concept introduction:

The error associated with the experimental value is the difference of the experimental and accepted value.

$\text{Error}=\text{experimental}\text{value}-\text{accepted}\text{value}$

Percent error represents the error as the percentage of the accepted value.

$\text{Percent}\text{error}=\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\times 100$

Answer to Problem 94A

The percent error value of density measurement of copper is $0.223\%$.

Explanation of Solution

The percent error can be calculated by using the below. The experimental value is $\text{8}\text{.98}\text{g/mL}$ while the accepted value is $\text{8}\text{.96}\text{g/mL}$.

$\begin{array}{c}\text{Percent}\text{error}=\left(\frac{\left|\text{experimental}\text{value}-\text{accepted}\text{value}\right|}{\text{accepted}\text{value}}\right)\times 100\\ =\left(\frac{\left|\text{8}\text{.98}\text{g/mL}-\text{8}\text{.96}\text{g/mL}\right|}{\text{8}\text{.96}\text{g/mL}}\right)\times 100\\ =\left(\frac{\left|0.02\text{g/mL}\right|}{\text{5}\text{.5 g/mL}}\right)\times 100\\ =0.223\%\end{array}$

Hence, the percent error is $0.223\%$.